DE60132490T2 - METHOD FOR TRANSMITTING A WAVEFORM WITH CONTROLLABLE DAMPING AND SPREAD SPEED - Google Patents

Abstract

Methods for driving a lossy transmission media with an energy wave defined by a an exponential waveform function. The propagation delay and attenuation of the wave is a function of an exponential coefficient, and its propagation velocity is essentially constant and independent of displacement. Utilizing relationships between the propagation velocity, exponential coefficient, attenuation, and transmission line parameters, one may effectively model various transmission media. One may also determine unknown transmission line parameters, waveform exponential coefficients, attenuation, and/or propagation velocities by utilizing those relationships. By modulating the exponential coefficient, information may be encoded onto a waveform.

Description

transmission lines with their characteristic signal loss as well as their inherent time delay can cause problems in the design of systems that prepare multiple signals use that a delay and distortion. Modern computers are, for example, systems that have multiple electrical Use signals, and for which transmission line characteristics, such as B. delay, considered Need to become. Both digital computer chips and the circuit boards for connection The signals of these computer chips may have transmission line effects exhibit.

typical Show signals when used to generate input signals in transmission lines are generally delayed or propagation times that are not easily ascertainable. The Propagation speed of these waves is also with the local Shift along the transmission line variable.

A change or modification of the delay An electromagnetic transmission line usually includes the change the physical length the line; the change the width, the thickness and the distance of the pipe; the modification the capacity the line at points spaced along the line; or the change the transmission line by change the dielectric constant of the media surrounding the conductor. None of these procedures leads but by itself to applications where it would be desirable can, the propagation time of a lossy transmission line to change the applied momentum to change or otherwise modify it.

The current transmission line technology is based on the theory of lossless transmission and assumes that the pulse propagation velocity along a transmission line is constant. This assumption restricts however, significant design options for the implementation of delay lines in electronic circuits. In particular, delay lines become currently by extending the signal path (so that the signal takes a longer time to to arrive at a destination) or by the addition of an additional one implemented active circuit for slowing down a signal. In In any case, the change of the delay amount difficult and / or expensive as a redesign or a change the circuit requires. Furthermore, there is often no way to control the delay to change based on different input conditions. Therefore would it be beneficial, considering the ability would have, a delay line to implement, which controllable a delay time or mitigation could vary on the basis of different input conditions, and which could be implemented easily and inexpensively.

Currently known method for measuring transmission line parameters such as B. resistance, inductance, capacity and conductivity typically require special gauges that can be very expensive. Therefore would it be advantageous, over the ability to dispose of such parameters in a simple manner, for example, under Application of cheap multi-purpose measuring instruments, which in general available in electronics labs stand, such. An oscilloscope or signal waveform generator.

Of the delay amount in networks including broadband networks, is often a major design factor. current Design techniques for the analysis of the length the delay in non-inductive and inductive transmission line networks are notoriously inaccurate; therefore it would be beneficial to know about the ability to dispose of a simple formula to calculate the total delay or the attenuation in non-inductive as well as inductive networks with a high Accuracy grade to use. It would also be advantageous if Such a method is used in computer assisted design (CAD) systems could be.

SUMMARY OF THE INVENTION

In one aspect, the invention is a method of transmitting a waveform at a substantially constant propagation velocity along a transmission line. As used herein, "waveform" is generally intended to be read in the meaning of any energy signal or its representation. As used herein, "transmission line" is to be read generally in the meaning of any medium capable of transmitting a particular waveform. Transmission line may refer to a wide range of media including, but not limited to, electrically conductive and mechanically oscillating media. According to the method, an exponential waveform is generated. The exponential waveform is determined by an exponential coefficient α. The waveform is applied to the transmission line to the waveform at a substantially constant propagation velocity and the propagation speed depends on α and a transmission parameter of the transmission line. As used herein, "transmission parameter" is generally intended to be read as any distinguishable characteristic of the media forming the transmission line.

In Further, the transmission parameter Induction, resistance, capacity, Conductivity or include any combination thereof from the transmission line. The transmission speed can of α according to several different equations, such. For example, but not limited to, the herein depend on. An attenuation coefficient The waveform may also vary from α according to several different ones Equations, such as B., but not limited to, the depend on it. The transmission line may include an electrical conductor. The transmission line can be a Include trace. The transmission line can be a delay line include. The transmission line can include a connection. The transmission line can be include acoustic medium. The transmission line can be Include diffusion medium. The procedure can also be a change of α as Include response to an input signal to the waveform generator. The method can also determine the propagation velocity and the calculation of the transmission parameters using the propagation velocity and the exponential coefficient include. The determination of the propagation speed can receiving propagation information from the transmission line using one or more connected to the transmission line Receive elements include. The one or more receiving elements can include a threshold detector. The procedure can also the determination of an impedance discontinuity of the transmission line and its Place using the exponential coefficient, the propagation velocity and the transmission parameter include. The method may also include the change of the exponential coefficient α, to encode information on the waveform. The procedure can also the surveillance a modulated propagation velocity for decoding Information include. The procedure can also be monitoring modulated attenuation information for decoding the information.

In In another aspect, the invention is a method of transmission a waveform along a transmission line. An exponential waveform is generated. The exponential waveform is through an exponential coefficient α. The waveform will be sent to the transmission line applied to transmit the waveform so that an attenuation constant the waveform of α and a transmission parameter the transmission line depends.

In In another aspect, the method may also include determining an impedance discontinuity the transmission line and their location using the exponential coefficient, the Attenuation constant and the transmission parameter include.

In In another aspect, the invention is a method of calculation the transmission characteristics an unknown waveform of two known waveform transfer characteristics. An exponential waveform is constructed so that they pass along a transmission line transmitted at a substantially constant propagation speed can be. The propagation speed depends on a transmission parameter the transmission line and an exponential coefficient from the waveform. The transmission parameter defines a first unknown waveform transfer characteristic that Propagation velocity defines a second unknown waveform transfer property, and the exponential coefficient defines a third unknown Waveform transmission characteristic. One of the three unknown waveform properties is calculated by the remaining two of the three unknown waveform transfer characteristics two known waveform transfer characteristics be equated.

BRIEF DESCRIPTION OF THE DRAWINGS

The The following drawings form a part of the present description and are attached to certain aspects of the present invention in more detail to demonstrate. The invention may be better understood by reference to one or more of these drawings in combination with the detailed description of the specific embodiments presented herein be understood.

1A and 1B FIG. 15 are graphs illustrating positive exponential waveforms over a time interval T. FIG.

2 FIG. 4 is a general block diagram of an apparatus for generating positive exponential waveforms in accordance with the present disclosure. FIG.

3 FIG. 12 is a circuit diagram of a circuit for generating a positive exponential waveform according to the present disclosure. FIG.

3B FIG. 12 is a circuit diagram of a circuit for generating a positive exponential waveform according to the present disclosure. FIG.

4 FIG. 12 is a circuit diagram of a circuit for generating a positive exponential waveform according to the present disclosure. FIG.

5 FIG. 12 is a circuit diagram of a circuit for generating a positive exponential waveform according to the present disclosure. FIG.

6 FIG. 10 is a block diagram of an apparatus for generating a positive exponential waveform according to the present disclosure. FIG.

7A FIG. 12 is a block diagram of a waveform generation circuit in which both the rising and falling edges of a waveform are positive exponential functions in accordance with the present disclosure.

7B Figure 4 is a graphical representation of illustrative waveforms with positive rising and falling edges.

8th FIG. 12 is a graph illustrating the input signal (left curve) and output signal (right curve) of a long coaxial transmission line operated by a limited positive exponential waveform according to the present disclosure.

9 FIG. 12 is a graph illustrating the transit time (t _of ) versus the exponential coefficient alpha (α) for a long coaxial transmission line in accordance with the present disclosure. FIG. In this figure, reference to HSPICE in the legend refers to a commercial circuit simulation software package developed by Avant! Corp. (46871 Bayside Parkway, Fremont, CA 94538) and has a website at www.avanticorp.com.

10 FIG. 12 is a table of experimental results of driving a 30.5 m (100 feet) coaxial transmission line having a positive exponential waveform with a variable exponential coefficient alpha (α according to the present embodiment.

11 FIG. 10 is a sketch of a transmission line and a test connection according to the present disclosure. FIG.

12 FIG. 12 is a circuit diagram of an input signal pulse waveform generator according to the present disclosure. FIG.

13 FIG. 10 illustrates a threshold detector in accordance with the present disclosure. FIG.

14 FIG. 12 illustrates a circuit diagram of an exponential waveform pulse generator according to the present disclosure. FIG.

15 FIG. 10 illustrates a conceptual design of the entire measurement setup to perform principle-proofing experiments according to the present embodiment.

DESCRIPTION OF ILLUSTRATIVE EMBODIMENTS

The presently disclosed methods and systems include the ability to vary the propagation speed and attenuation of one or more signal pulses in transmission lines. According to the methodology described herein, the propagation velocity and attenuation of a pulse in a lossy transmission line depends on the shape of the signal applied to the line. The propagation speed and attenuation can be controlled by controlling the shape of the signal. In particular, it has been found that when an exponential signal is applied to a lossy transmission line, the resulting propagation velocity and attenuation from an exponential coefficient (the coefficient may be positive or negative) of that signal hangs. With a constant exponential coefficient, the propagation velocity is essentially constant. A change in the value of the exponential coefficient produces a controllable propagation velocity and attenuation of the variable signal.

aid of this revelation an adjustable delay line (and an adjustable attenuation line) using one or more exponential pulse signals as Input pulses in a transmission line circuit be implemented. The amount of delay can be controlled, without modifying signal paths, be changed by the shape changed the input pulse signal becomes. In particular, the delay can by changing of an exponential coefficient of an exponential waveform. The ability, delay times to control, provides an improved method of reduction timing offsets in many different types of circuits ready.

It has also been found that the delay speed and attenuation an exponential waveform not only of its exponential coefficient, but also of different transmission parameters the transmission line depends. For example, it has been found that resistance, inductance, capacitance and conductivity a transmission line with the propagation velocity and an exponential coefficient an exponential waveform. Because the speed and mitigation an exponential pulse waveform from the waveform as well as from the transmission line parameters depends can the line parameters by measuring the response of a line Exponentialsignale different forms are determined. Characteristic transmission line parameters can be evaluated by the propagation speed or signal attenuation under Using a known exponential coefficient is calculated, to resolve them according to an unknown line parameter. alternative can the propagation velocity or signal attenuation is evaluated by using a known exponential coefficient and known transmission line parameters become. Alternatively you can an exponential coefficient by measuring a propagation velocity or signal attenuation a line with known transmission line parameters be calculated.

In order to obtain parameters of a lossy transmission line, a test piece of a transmission line segment with a length L can be operated with an input voltage having a function such. B. De contains ^αt , which alternately uses two different values of the exponential coefficient α. At each α, a measurement of the propagation time t _of (where "of" means a "runtime") can be performed, and the propagation velocities can be calculated using v = t _of / L. Simultaneous equations (exemplary equations are discussed in more detail below) having one or more conduction parameters along with α and velocity v can then be used along with measured values of α and v to determine one or more conduction parameters.

aid of the present invention current interconnection modeling techniques of integrated circuits be improved because simple formulas can be used to the total delay or signal attenuation both in non-inductive and inductive transmission networks with a high To calculate degree of accuracy. With known relationship between an exponential coefficient of a waveform of the input signal, Propagation speed or signal attenuation and one or more transmission line parameters you can more accurately time delays or signal attenuation within a circuit or set of coupled transmission line circuits model. Furthermore, one can with known transmission line parameters a desired one Calculate exponential coefficients, which when applied to a transmission line is applied, a desired Delay Time or a desired one signal attenuation generated. The present disclosure will become a person skilled in the art understand in this field that these results are coupled to Circuits including coupled transmission lines can be applied.

aid The present disclosure includes other applications which use an exponential waveform, but are not limited to the controllable change a propagation speed and attenuation of an electromagnetic plane and / or spherical Wave in electrically lossy media; the controllable change a propagation velocity and attenuation of sound waves in lossy ones acoustic media, such as. As viscous and relaxing gases, fluids and solids; and the implementation of a signal modulation in lossy communication links in which information is transported by a controlled change in the rate of propagation and / or signal attenuation monitored becomes.

The Operation of the present disclosure will become better understood by reference understandable on equations, which is the propagation of a signal along different media describe. The behavior of certain transmission lines can be through the line equation will be described. Different versions the line equation with an exponential waveform of the input signal according to the present Revelation are listed below. Throughout these revelations become solutions of various equations referred to as "SD" solutions. With "SD" or "sd" is "Speedy Delivery" (fast delivery) meant, which is a term coined by the inventor, to equations to describe the advantageous properties disclosed herein provide. In particular, the SD solutions are waveforms that are included a speed and with a weakening that can be transmitted of an exponential coefficient and one or more line parameters depend.

The exponential coefficient, which allows SD solutions, can be positive or negative, and the waveforms can propagate in the positive or negative direction. For simplicity, in the examples below, the exponential coefficient is assumed positive and the waveforms propagate in the positive direction. With regard to electrical transmission lines, the four parameters occurring in the line equation are R Resistance per unit length, L Inductance per unit length, C - Capacity per unit length and G - Conductance per unit length.

The first version of the considered line equation does not have vanishing values for R and C ,

1. RC line

The line equation in this case is:

wobei v(0, t) = De^αt die SD-Grenzbedingung ist.The SD equation is

where v (0, t) = De ^{αt is} the SD boundary condition.

oder die Ausbreitungsverzögerung dieser Welle pro Einheitsdistanz ist

wobei

ist. Somit hängen die Ausbreitungsgeschwindigkeit v und die Verzögerung pro Längeneinheit von dem Parameter

ab. Die Abschwächung dieser sich ausbreitenden Welle wird beschrieben durch:

The propagation speed of this wave is

or the propagation delay of that wave per unit distance

in which

is. Thus, the propagation velocity v and the delay per unit length depend on the parameter

from. The attenuation of this propagating wave is described by:

ebenfalls von

bhängig. Thus, the dispersion coefficient

also from

epending.

Of the Electricity in a transmission line enough the same partial differential equation as the stress. The SD current waveforms have the same shape as the voltage and thus, the SD current pulse has the same controllable propagation velocity and attenuation characteristics like the tension.

2. Diffusion

wobei T(x, t) die Temperatur in dem Festkörper an dem Punkt x und zu dem Zeitpunkt t ist. Der Koeffizient k ist die Diffusivität.The previous example of the line equation has the same form as the diffusion equation, which many physical phenomena such. Thermal conduction and other forms of transport of matter resulting from random molecular motions, as known in the art. The SD results of the x-direction heat conduction in an isotropic solid can be represented as follows:

where T (x, t) is the temperature in the solid at point x and at time t. The coefficient k is the diffusivity.

The SD solution is

The propagation velocity of this heat wave is v = √ αk with the attenuation coefficient √ α / k ,

Third RLC -Management

und die SD-Gleichung umfasst:

The line equation in this case is:

and the SD equation includes:

oder die Ausbreitungsverzögerung pro Längeneinheit ist

oder The propagation speed of this wave is

or the propagation delay per unit length

or

und der Abschwächungskoeffizient ist

welcher ebenfalls von α abhängt.Again v (or τ) depends on α (or τ _sd ). The weakening is described by

and the attenuation coefficient is

which also depends on α.

4th CLG -Management

Another version of the line equation does not have vanishing values for G . L and C :

oder,

und der Abschwächungskoeffizient ist.This has the same shape as the one above ( RLC ) Case, where the propagation velocity, the delay per unit length and the attenuation expressions are replaced by RC by LG obtained in the previous results.

or,

and the attenuation coefficient is.

5. Propagation of an electromagnetic plane wave in a lossy medium

und dieselbe für HZ

wobei μ die elektrische Permeabilität des Mediums repräsentiert, ε die elektrische Permittivität des Mediums repräsentiert und σ die elektrische Leitfähigkeit des Mediums repräsentiert.The propagation of an electromagnetic plane wave in the x-direction and with the field components E _y and H _z can be described by two equations:

and the same for HZ

where μ represents the electrical permeability of the medium, ε represents the electrical permittivity of the medium and σ represents the electrical conductivity of the medium.

mit dem Abschwächungskoeffizienten

A comparison of these equations with the line equation of the same form with non - vanishing values for C- , - L and G Parameter shows an analogous set of relationships: CLG transmission line Level EM wave in lossy medium V (volts) E (volts) I (ampere) H (ampere) C (Farad / m) ε (Farad / m) L (Henry / m) μ (Henry / m) G (Siemens / m) σ (Siemens / m) and, the propagation speed of the SD solutions is for E _y and H _z

with the attenuation coefficient

Another version, with only L and G are not zero, is analogous to that RC Case, where LG RC replaced in the expressions for the speed, time delay and attenuation of the propagating wave.

und die SD-Wellenlösung enthältThe results for all four parameters with non-vanishing values follow. The line equation in this case is

and contains the SD wave solution

und die Verzögerung pro Längeneinheit ist

oder

und die Abschwächung dieser Welle istThe propagation speed of this wave is

and the delay per unit length

or

and the weakening of this wave is

Thus, the attenuation coefficient is

Again, the propagation velocity, the delay time per unit length and the attenuation of the wave depend on α (or τ _sd ).

6. Complex frequency-dependent parameters

The transmission line parameters are frequency dependent in some applications. Some examples are, though R = R (s) due to penetration depth effects, L = L (s) is because current return paths are frequency dependent, and G = G (s) resulting from frequency dependent electrical losses. As used herein, "s" denotes a complex variable.

und die Ausbreitungsgeschwindigkeit dieser Welle ist

mit der Abschwächung

The SD solution for the four parameter line equation with frequency dependent effects in the four parameters R (S), L (S), G (S), C (s is

and the propagation speed of this wave is

with the weakening

Of the attenuation coefficient is

7. Spherical waves in three-dimensions

durch den Laplace-Operator V ² ersetzt wird. Wir veranschaulichen die Verallgemeinerung auf den 3D-Raum unter Verwendung des Beispiels der Ausbreitung einer elektromagnetischen Welle. Wenn die elektromagnetischen Wellen abgehende sphärische Vektorwellen sind, d. h., wenn die Lösungen E_θ = E_θ(r, t) und H_ϕ = H_ϕ(r, t) Funktionen des radialen Abstandes (r) und der Zeit (t), aber nicht der Winkelkoordinaten θ, ϕ sind, genügen dann die vorstehend beschriebenen SD-Gleichungen, modifiziert durch Division mit dem radialen Abstand r, den erzeugten 3-dimensionsionalen Ausbreitungsgleichungen, wenn in allen Versionen der Leitungsgleichung

durch

ersetzt ist. Somit genügen rE_θ(r, t) und rH_ϕ (r, t) derselben Leitungsgleichung wie zuvor, wobei x durch r ersetzt ist. Die Ausbreitungsgeschwindigkeiten der sphärischen Vektorwellen entlang der radialen Richtung sind dieselben wie die, die vorstehend für die Ausbreitung entlang der x-Achse erhalten wurden. Die Wellenformabschwächung hat den Einfluss des zusätzlichen 1/r-Faktors, sowie dieselbe vorherige α-Abhängigkeit in dem abfallenden Exponential-Koeffizienten. Es werde die sphärisch symmetrische drei-dimensionale Version der elektromagnetischen Wellengleichung für E_θ betrachtet.The different versions of the line equation can be generalized to a 3D space by using the formula

through the Laplace operator V ^{2 is} replaced. We illustrate the generalization to the 3D space using the example of the propagation of an electromagnetic wave. If the electromagnetic waves are outgoing spherical vector waves, ie, if the solutions E _θ = E _θ (r, t) and H _φ = H _φ (r, t) functions of the radial distance (r) and the time (t), but are not the angular coordinates θ, φ, then the above-described SD equations, modified by dividing by the radial distance r, satisfy the generated 3-dimensional propagation equations, if in all versions of the line equation

by

is replaced. Thus, rE _θ (r, t) and rH _φ (r, t) satisfy the same line equation as before, where x is replaced by r. The propagation velocities of the spherical vector waves along the radial direction are same as those obtained above for propagation along the x-axis. The waveform attenuation has the influence of the additional 1 / r factor, as well as the same previous α-dependency in the decaying exponential coefficient. It will consider the spherically symmetric three-dimensional version of the electromagnetic wave equation for E _θ.

und das Herauskürzen der 1/r-Terme ergibt dieselbe Leitungsgleichungsform wie zuvor. Somit ist die SD-Lösung

und die Ausbreitungsgeschwindigkeit im 3D-Raum entlang der radialen Richtung ist

welche dieselbe Form wie die zuvor für die Ausbreitungsgeschwindigkeit in dem eindimensionalen Falle entlang der x-Achse ist. Die Größe von E_θ(r, t) und H_ϕ(r, t) nehmen mit als 1/r ab.Since r is constant, is

and truncating the 1 / r terms gives the same line equation form as before. Thus, the SD solution

and the propagation velocity in 3D space is along the radial direction

which is the same shape as before for the propagation velocity in the one-dimensional trap along the x-axis. The size of E _θ (r, t) and H _φ (r, t) decrease with 1 / r.

and the exponential decay coefficient

8. Results for other forms of lossy wave equations

wobei:

ξ

= Partikelauslenkung aus der Gleichgewichtsposition entlang der x-Achse,

c

= die Ausbreitungsgeschwindigkeit der Welle in dem Medium ohne Viskosität ,

R

= effektive Viskosität,

ρ₀

= konstante Gleichgewichtsdichte des Mediums ist.

The SD results extend to other forms of lossy wave equations that do not match a version of the line equation. One such case is acoustic plane waves traveling in a viscose absorption medium. In this case, the lossy wave equation is the same

in which:

ξ

= Particle displacement from the equilibrium position along the x-axis,

c

= the propagation velocity of the wave in the medium without viscosity,

R

= effective viscosity,

ρ ₀

= constant equilibrium density of the medium.

und die Ausbreitungsgeschwindigkeit ist

mit der Wellenformabschwächung

The SD wave solution for this equation is

and the propagation speed is

with the waveform attenuation

Frequency-dependent parameters are accommodated here in the SD propagation speed and the attenuation in the same way as they were in the line equation. That is, if c = c (s), then the above expressions for v and the attenuation are modified by modifying c ² by c ² (α).

mit der AbschwächungA second example of an acoustic wave is the propagation of sound in a chemically reacting fluid consisting of two or more constituents (such as seawater). The following example represents a fluid with two components: τ (P tt - c 2 ∞ P xx ) t + (P tt - c 2 0 P xx ) = 0 where c _∞ and c _{0 are} the velocities at infinite frequency and zero frequency, τ is the relaxation time associated with the chemical reaction of the two components, and P is the sound wave pressure. The SD propagation speed of this sound wave is

with the weakening

The above discussion of methods of using SD waveforms for controlling the propagation velocity and attenuation of acoustic waves can be applied to extract information which are viscous, acoustically absorbing media and chemically reactive characterized by acoustic media. In particular, you can by measuring the propagation velocity with a known exponential coefficient determine one or more acoustic parameters.

wobei T(x, t) die Temperatur entlang der Leitung (oder dem Stab) ist, κ die thermische Diffusivität ist, K die thermische Leitfähigkeit ist und A die Querschnittsfläche der Leitung (Stabes) ist. g(t) repräsentiert die angenäherte Green-Funktion der thermischen Leitung aus der(m) erwärmten Leitung (Stab) in das Substrat unter Weglassung der räumlichen Abhängigkeit.Another example of lossy propagation in a thermal problem that does not conform to a version of the line equation is a partial differential-integral equation describing the temperature compensation process that results from heat conduction along a microstrip or a well-conductive one in a substrate lower conductivity buried bar results in:

where T (x, t) is the temperature along the conduit (or rod), κ is the thermal diffusivity, K is the thermal conductivity, and A is the cross-sectional area of the conduit (rod). g (t) represents the approximate Green function of the thermal conduction from the (m) heated line (bar) into the substrate, leaving out the spatial dependence.

mit der Ausbreitungsgeschwindigkeit

und die Wellenformabschwächung istThe SD wave solution of this equation is (G (s) is Laplace transform of g (t)

with the propagation speed

and the waveform attenuation is

In An embodiment employing the above methodology may use an exponential wave be generated by locally a material such. As a rod or a trace with a laser beam or another source is heated, and the beam along a path, such. B. one Rod or a track, at a constant speed is moved. In such an embodiment, the resulting temperature profile is along the path (which can be a rod or track) an exponential waveform (T (x) t of the form shown above, which varies with speed of the moving localized heat source.

Similar Demonstrations of the currently disclosed methodology can be found in other media are represented by the solution of the stable state for differential equations, including records considered coupled equations which is the wave propagation of an exponential waveform in this media describes. For additional media may have an input signal waveform with an exponential coefficient and the corresponding propagation equations can solved accordingly be the relationship between the exponential coefficient, the propagation velocity, the wave attenuation and one or more transmission line parameters to investigate. The solution such propagation equations using a known Input signal waveform can be applied using a variety in Subject area mathematical methods are achieved.

The transfer of energy signals according to the present invention Revelation allows also the control of the penetration depth of propagating waves in three-dimensional media through the control of α. In the case a transmission of signals in electromagnetic transmission lines allow the Methods and systems of the present disclosure include control the penetration depth of line currents in the conductive structure a transmission line. A similar Control of the penetration depth of propagating energy signals in three-dimensional media, using the present disclosure energy signals other than electromagnetic, such as B., but not limited to thermal, diffusing or acoustic ones.

For applications, in which the signal is non-electromagnetic, you have a Use transducers to provide an electrical, as known in the art Signal in for to convert a special application suitable. Such a converter can in a feedback loop with a power amplifier which, as known in the art, for operating the Converter is used. In other applications, a converter perform an impedance match to an electromagnetic line, or convert a voltage signal into an acoustic signal. converter for different transmission media are commercially available and examples include loudspeakers, piezoelectric devices, Antennas, thermal heating elements and any others in the art known converter.

1A and 1B Examples of exponential waveforms that may be used in accordance with the methods and systems described herein. The waveform of 1A is a positive exponential waveform with an initial condition of 0 and with different maximum amplitudes those shown with dashed lines. The waveform in 1B is a positive exponential waveform with an initial value of D and different maximum amplitudes, shown with dotted lines.

As will be apparent to one of ^{ordinary skill in the art} , the input signals used in the present invention need not be equal to De ^αt , and in a more general case, a suitable input signal ^waveform may be represented by a function such as a. B. but not limited to the same:
V _in = De ^αt + A + f (t), where f (t) does not contain the form e ^αt .

The additive function f (t) brings no deviation from the solution of the different wave equations, such. The equations discussed above. Over time, the term containing e ^αt dominates the solution of the stable state, and the characteristics of the propagation ^wave are as described herein. The constant "A" can be used to set waveform initial conditions and may therefore prove useful in many applications.

There Positive exponential waveforms can increase steadily, making practical considerations the need to generate the waveform at a certain level, which is determined by the specific application to crop or limit. The circumcision can be done by different methods can be achieved, as is known in the art.

The Use of a positive exponential function as a disturbance function at an input of a transmission medium requires the generation of a suitable signal. You can do one Exponential waveform, which is used for generating a constant Propagation speed is suitable as described herein, and this exponential waveform can, as known in the art of electronics, on different Species are generated. For example, you can use a waveform with a single jump with a positive exponential function over one Time interval T generate, or you can use repetitive waveforms with repetitive ascending, descending or ascending and use falling edges through a positive exponential function are defined. Positive exponential waveforms can become prove difficult in practice, as they theoretically have no limit increase. In practical applications, the exponential component over a certain time interval are created and after this interval For example, the signal may be clipped or trimmed as known in the art be returned to an initial value. Termination or truncation of the waveform is completely arbitrary and is merely a necessity of special applications and is not required by the present invention.

2 illustrates in block diagram form a system that can be used to generate suitable waveforms. Two feedback loops are for the block diagram in 2 shown. The feedback loop 109 can be used when a transducer output signal is forced to follow an input voltage. The feedback loop 108 can be used if a measured parameter is fed back to control the exponential coefficient α. The device 105 FIG. 10 illustrates a composition of functions for receiving, detecting, processing, and returning information to a generator for modifying the output of the exponential generator.

One One skilled in the art will recognize that there are several methods for generating an exponential waveform generating circuit gives. Circuits for generating negative exponential waveforms are common. However, those that generate positive exponential signals are Rare. Three circuits for general waveforms can especially for the implementation of embodiments described herein useful and are presented below.

Circuit Methodology 1

The methodology 1 uses waveforms resulting from the solution to the differential equation:
Formula result: v (t) = k (d) v (t) / dt)

3A and 3B provide block diagrams of the circuit methodology 1 and an operational amplifier circuit solution 241 may be used in at least three different configurations to provide an inverting summing amplifier 200 , an inverting integrator 202 and amplifiers 104 to create. resistors 231 and 230 can increase the gain of the jump input signal 204 which starts a positive exponential ^{component of} the general form De ^αt . The Kon capacitor 234 can through a FET 200 be held in a reset state until an input signal 204 starts a cycle. The output signal of the summing amplifier 200 can be an amplifier 104 which inverts and amplifies the signal to produce a positive exponential waveform. diodes 237 . 238 and 239 can be a bidirectional limiting network in the feedback of the amplifier 104 form. The diodes 237 and 239 are zener diodes whose zener voltages can be varied to change boundary areas. The voltage at the positive input of the amplifier 104 can be changed to change the lower limit. The circuit in 3B is one embodiment of a circuit that can be used to solve the differential equation whose solution is a positive exponential function over time.

Circuit Methodology 2

Method 2 uses a diode that has a current that is a positive exponential function of a voltage V _d , and makes V _d a linear time function, and uses the resulting current to generate a voltage that is a positive exponential Function over time.

4 provides a schematic diagram of the circuit methodology 2 dar. A triggered ramp generator 401 with an offset voltage 402 clamps the diode 400 to the switch-on threshold. The gate signal 403 starts the linear ramp, which generates a diode current that is a positive exponential function over time, and which generates a similar voltage when it enters the resistor 404 flows. 5 FIG. 12 illustrates an embodiment in which the diode current as a function of voltage may be utilized to implement a positive exponential voltage over time.

A power source 602 charges the capacitor 601 on when the transistor 600 is off. A resistance 603 can the transistor 601 pretension close to the switch-on point. The current in the transistor 607 can through the transistors 604 and 605 be reflected, and in turn flows through the resistor 606 to generate an output voltage. The connection of the transistors 604 and 605 is a configuration commonly referred to as a current mirror. When the transistor 600 is off, the capacitor charges 600 linear because the base current is small. The voltage across the base emitter junction of 607 is a linear ramp voltage and the collector current in 607 is a positive exponential function over time. The transistors 604 and 605 reflect this current to the positive exponential voltage across the resistor 606 to create. Changing the threshold value of the waveform can be achieved by increasing or decreasing the power supply voltages.

Circuit methodology 3

The methodology 3 generates a sequence of digital numbers representing the positive exponential function 802 represent. This sequence can then be converted via a digital / analog converter into an analog signal.

6 provides a circuit for generating a positive signal using a processor 800 and a D / A converter 801 This general method can be used to generate any voltage V = De ^αt + A + f (t) by using a suitable program to generate the required digital number sequence. A number sequencing processor may be one of the many memory programmable controllers including computers, microcomputers, microprocessors, controllers, or microcontrollers. Although the circuit methodology 3 may be suitable for the generation of arbitrary waveforms, the generated signals may be limited by the clock frequency of the memory program device in the bandwidth.

An embodiment used to generate a positive exponential decaying edge requires a voltage subtraction process. 7A and 7B show a block diagram of a positive exponential function with two edges. A tension 701 Switches a voltage expander 100 with an output signal e ^αt -1 which is limited 101 , and to a summing circuit 700 is applied to a tension 704 to create. This tension is through 104 for generating an output signal 705 strengthened. At a certain time t ₁ , the voltage switches 702 another voltage exponent generator 100 with an output voltage defined by e ^αt -1, which is limited, and from the voltage to the positive input of the summing circuit 700 is subtracted. During the falling edge of the output signal of the summing circuit is a voltage 704 defined by 2 - e ^αt . At t ₂ , the subtraction can be stopped and at a time t ₃ , the process can be repeated.

The Examples below are attached to preferred embodiments to demonstrate the invention. It should be obvious to one skilled in the art be seen that disclosed in the following examples Represent techniques, techniques, that of the inventor as good in the practice of the invention have been properly disclosed, thus as specific species for your Practice implementation can be considered. The expert on this Territory is likely however, given the present disclosure, many changes will be apparent in the specific embodiments, which are disclosed performed can be and this nevertheless an equal or similar result without deviation achieve the spirit and scope of the invention.

example 1

The circuit methods described herein may generate a power wave as a voltage and may be applicable to various wave propagation media with a suitable transducer. The experimental verification of the disclosed method was carried out using an exponential function of the form De ^αt . The signal was generated for use on a long coaxial transmission line using method 3 above. The generated positive exponential signal was applied to a 30.5 mm (100 feet) coaxial transmission line to verify the disclosed method. 8th and 9 represent some of the results in the verification tests. 10 is a table of experimental results.

Example 2

SD Modulation

information may be in a lossy medium (eg, using electrical transmission lines, acoustic waves, or electromagnetic waves) under application of SD waveforms as disclosed herein and modulating α with a Code pattern for transporting a message. A receiver can The changes in the propagation velocity or the attenuation coefficient measure the waveform to decode the message. The measuring task the propagation speed of the receiver can be implemented by passing threshold measurement intervals of consecutive waveforms measured at two points separated by a known distance. The threshold timing measurements may yield wave propagation velocity information. what estimates from α the analytic relationship of the wave propagation velocity and α.

One alternative detection method can measure the attenuation coefficient of an SD wave by: Amplitude or pulse area measurements the propagation wave at two or more by known routes separate locations are measured. Another implementation of this Type of modulation can be the transmission an SD wave over involve long journeys through a medium of low loss, which then by a receiver can be detected, a short path with highly lossy transfer material contains. The propagation speed through the short lossy one Path of the recipient can then be monitored by using threshold time measurements along the path be transferred to the Decode message. Alternatively, the SD wave attenuation within the lossy transmission path Recipient which gives the modulated pattern of a. If both the SD wave propagation velocity as well as the attenuation exponent can be measured by the detector, then the product of this two sizes directly give the value of the exponential coefficient α.

Example 3

circuit test

Current designs of high speed package-to-system digital transmission circuits at both chip and system level require consideration of maximum frequencies from 300 MHz to 1 GHz. Thus, circuit designs are transmission lines and the development of this technology requires design verification through experimental fast circuit testing and measurement systems. Current test and measurement system development does not break with the rapid changes in interconnect technology. There is great concern in the industry that this delay in circuit test technology may delay the growth of interconnect technology. Many realize that a greater increase in research and development effort in completely new test methodologies is needed to address the situa to clean up.

A new circuit test methodology is provided by the present disclosure provided. This test methodology is based on the use of impulses with variable speed, which by means of simple threshold detectors be detected and timed at one or more Digits in the circuit are connected. The speed change The propagating impulse can be generated by a measurable shape parameter be controlled in the applied input pulse waveform of the circuit. This input form parameter and the resulting propagation pulse velocity, the obtained from the threshold detectors are the only ones Measurements required to give a simple equation calculate which characteristic parameters of the transmission line supplies.

A detector is sufficient to measure the pulse transit time when the threshold times of an incident and reflected response pulse are measured at a single location in the line. In this case, if the line and pulse shape parameters are known, the calculated pulse rate and attenuation along with the measured pulse round trip time determine the location and numerical evaluation of the line error or impedance discontinuity which causes the pulse reflection. A conceptual sketch of a transmission line showing two test connections is in FIG 11 shown. An input pulse waveform and two threshold detectors are shown. The threshold detectors of 11 determine the time at which a propagating pulse reaches a threshold at the monitor positions of the detector along the line. The input pulse waveform requires an exponential form specially tailored for this test procedure. A waveform generator generating this type of pulse (α> 0) is in 12 shown. It contains a jump generator followed by an exponential waveform generation circuit.

That by the waveform generator of 12 to the input line of 11 applied input signal can be in 13 generate threshold level detector input signals e ₁ (t) and e ₂ (t). In 13 T is the signal threshold setting of the threshold detectors, and t ₁ and t ₂ are times measured by the threshold detectors at which e ₁ and e ₂ pass the threshold level. The pulse propagation velocity v can be measured by the ratio (t ₂ -t ₁ ) / l, where 1 is the separation distance between the threshold detectors along the line.

in Beziehung.The transmission line of this example is considered by the version of the line equation with three parameters: R (Resistance per unit length), L (Inductance per unit length) and C (Capacity per unit length), assumed. The input waveform exponent, α, and v are closed R . L and C by

in relationship.

Thus, conducting the conduction test twice with two different sets of (measured) values for α (α> 0) and v gives two equations of this form, which provide an estimate of RC and LC enable. By doing RC Case, a minimum of a test result is needed to determine the line parameter RC appreciate. A similar result can be obtained from transmission lines passing through all four parameters R . C . L and G as will be apparent to one of ordinary skill in the art using the present disclosure.

The Measurement of the attenuation coefficient in the change of α Answer is an alternative approach to the estimation of line parameters, since like the propagation speed also the attenuation coefficient in addition to the line parameters depends on α.

14 shows a representation of a suitable exponential waveform generator (EWG). 15 represents a configuration of an entire experimental measurement setup.

Example 4

VLSI and broadband housing connection design

Methods and systems disclosed herein may be used as a link delay measurement and optimization tool. An analysis according to the present disclosure provides a simple Also, line delay terms that are equally valid for all lossy variants of the four-parameter transmission line model of a connection, even those with frequency-dependent parameters that are important in the enclosure environment. The techniques utilizing this disclosure promise higher accuracy than those used in current CAD tools, as well as broader applicability to both on-chip and package environment.

Minimizing the connection delay on the chip

The delay of connections on high performance chips with lengths of about 1 mm to the dimension of the semiconductor chip are from the theory of lossy transmission line either using a low RLC line approximation Loss or for very resistive connection, an alternative approximation, which is based on an RC distribution model of the transmission line, neglected the inductive effects, estimated. The former estimate the delay at low loss is for currently proposed long low-impedance lines on a chip suitable, which are manufactured with a conductor geometry, the substantially larger in cross-section ("fat") than that according to submicron mass rules the current technology. The delay approximation of the RC line, which neglects inductive effects is only for the short ones suitable high-impedance connections, which are just long enough to To begin with, a significant transmission line behavior and not adequately modeled with concentrated models can be. But there is a big one Distance from longer ones resistive connections with line characteristics, which between these two delay estimation approximations currently only with time-consuming circuit simulations can be analyzed.

One Approach according to the present Revelation is neither to the very resistive nor the low-loss cases limited. Indeed The methodology disclosed herein provides a single consistent application Result, that for both extremes and all lossy cases in between are accurate.

One Example demonstrating techniques of the present disclosure includes a very resistive 15mm connection underneath Use of typical values for a 0.5 μm CMOS technology. (This connection line has a capacity per unit length (C) of 0.25 pF / mm, a resistance per unit length (R) of 18 ohms / mm and one inductance per unit of length (L) of 0.174 nH / mm at a relative dielectric constant from 4.0). The connection delay becomes conventional assuming approximate estimates for the delay the step response of an RC transmission line minimized when the receiving end of the line is not completed is.

The result for the conventional estimate of the minimized overall circuit delay is 753 ps for this example. Assuming ε _R = 4, would be a lossless 15 mm long terminated line a delay of (6.6 ps / mm) (15 mm) = 99 ps, or about 1/7 of the conventional estimate of the entire circuit of this high-impedance line to the Deliver chip. This large performance-limiting difference in the estimated versus ideal link delay may be referred to as the L ³ (Long Lossy Line) effect.

One way to reduce the delay of these long lines is to lower their resistance to that of "low loss" lines (defined as having a total resistance of less than two Z ₀₎ by making them to "fat" lines, the cross-sectional area of which is made substantially larger than the minimum dimension for the short lines on the device. This requires additional wiring levels on the chip to accommodate these "fat" lines with the corresponding yield and cost implications.

wobei D = 0,1 Volt und τ_SD = 10 ps unter der Annahme einer maximalen Treiberanstiegszeit (Chips mit 500 MHz-Taktraten haben Treibersignale mit Flankenanstiegszeiten bis zu 20 V/ns. Eine Skalierung auf 3 GHz Taktrate impliziert hier mit 100 V/ns vergleichbare Flankenanstiegszeiten). Das Ausgangsende von jedem der 5 mm Leitungssegmente wird als nicht abgeschlossen angenommen. Die Verzögerung des SD-Leitungssegments unter Annahme des Beispiels der RLC-Leitungsparameter und der Segmentlänge L_s ist 5 mm, ist

und ist gleich 47,2 ps. Die Verzögerung t_g des SD-Leitungstreiber ist 9,2 ps unter der Annahme, dass der Schaltpegel des Leitungsausgangssignal 50% des Eingangssignalmaximums ist, und dass die Leitungsausgangssignalspannung aufgrund des nicht abgeschlossenen Endes verdoppelt wird.Analysis of this compound using the present disclosure results in a much lower circuit delay of 169 ps, which is achieved using 35 mm sections and 3 SD drivers. The positive-exponential SD driver input signal may be generated with an unstable positive feedback loop (as currently found in high-speed analog ICs, cached comparators and memory cells) and may be represented by:

where D = 0.1 volts and τ _SD = 10 ps assuming maximum drive rise time (chips with 500 MHz clock rates have drive signals with edge rise times up to 20 V / ns. A scaling to 3 GHz clock rate implies comparable edge rise times with 100 V / ns). The output end of each of the 5 mm line segments is assumed to be unfinished. The delay of the SD line segment assuming the example of the RLC line parameters and the segment length L _s is 5 mm

and is equal to 47.2 ps. The delay _{tg of} the SD line driver is 9.2ps assuming that the switching level of the line output is 50% of the input signal maximum, and that the line output voltage is doubled due to the open ended.

The total SD connection delay is 56.4 ps × 3 = 186.9 ps, neglected every power-boosting Repeater. The comparable delay for this Connection example by means of conventional Method is 628 ps, which is the sum of 375 ps (RC load delay of the circuit the two drivers) plus 253 ps (RC transmission line delay estimate for jump voltage input signals to the two 7.5 mm unfinished line segments).

The SD results are less than 1/3 of the conventional minimized delay estimate for this L ³ compound. However, this improved result is still 2.5 times greater than the lossless (ideal) delay for the connection. Nevertheless, the reduction in line delay is significant, and if increases in the conductor cross-sectional area were required to reduce further delay, this increase in line geometry would be less pronounced. Alternatively, the delay of the SD line could (approximated to the lossless line delay) by a further reduction in the SC driver time constant, τ _sd can be further reduced. How well this limit is then reached can then be finally determined by how small the time constant of the SD driver can be made, and the limiting factor of the connection behavior is the design behavior of the SD driver.

The delay the SD connection is significantly lower than for two main reasons the conventional one Connection estimate the step response. First, the delay of the SD line driver significantly lower than the delay of the conventional RC line driver and second, includes the simple SD analysis the actual inductive effects of the wire, while the less accurate conventional RC analysis the step response does not do this. The less complex SD analysis determines the inclusion of the delay-reducing inductive Leadership effects, but the more complex conventional analytical analysis the step response of this long lossy line is not executable, if inductive and RC effects are included.

Summarized The present SD approach promises to link analysis a lossy line, significant improvements in VSLI design behavior Compared to those achievable with interpretations the conventional one Delay estimation method based. The SD analysis of compounds is more general in scope, and still less complex than analyzes that come from standard theory lossy transmission lines are derived.

LITERATURE REFERENCE

• 1. Carslaw and Jaeger, "Conduction of heat in solids ", Oxford University Press, 1959.
• 2. Crank, "The mathematics of diffusion ", Oxford University Press, 1975.
• 3. Jordan and Balmain, "Electromagnetic waves and radiating systems ". Prentice Hall, 1968
• 4. L.E. Kinsler and A.R. Frey, "Fundamentals of acoustics", John Wiley & Sons, Inc. 1962.
• 5. Moore, "Traveling-wave engineering, "McGraw-Hill Book Company, Inc. 1960.
• 6. Morse, D.M. and H. Feshback, Methods of Theoretical Physics, Part I ", McGraw-Hill Book Company. Inc. 1953.

Claims (7)

A method of transmitting a waveform having a substantially constant propagation velocity along a transmission line, the method comprises the steps of: (i) generating an exponential waveform, wherein the exponential waveform is truncated and the form De ^αt + A + f (t where t is time, D and A are constants, α is an exponential coefficient, and f (t) is a function of time, where f (t) does not include the form e ^αt ; and (ii) applying the waveform to the transmission line to transmit the waveform at a substantially constant propagation velocity, the propagation velocity being related to α and a transmission parameter of the transmission line, the method being further characterized by comprising one of the following steps : (a) changing α in response to an input signal to the waveform generator; or (b) determining the propagation velocity and calculating the transmission parameter using the propagation velocity and the exponential coefficient; or (c) determining an impedance discontinuity location of the transmission line and its location using the exponential coefficient, the propagation velocity and the transmission parameter; or (d) modulating the exponential coefficient α to encode information in a waveform. The method of claim 1, wherein the modulating step (d) further comprising one of the following steps: (d1) query the modulated propagation velocity around the information decode; or (d2) query the modulated attenuation um to decode the information. The method of claim 1, wherein the step (b) the step of receiving the propagation information from the transmission line using one or more receiving elements that to the transmission line coupled, wherein the one or more receiving element (s) include a threshold detector. The method of claim 1, wherein the transmission line either an electrical conductor, or a conductive wire, or a delay line, or a connection or acoustic medium, or a diffusion medium. The method of claim 1, wherein the transmission parameter the inductance, the resistance, the capacity or the electrical conductivity of the transmission line or any. Combination of it. The method of claim 1, wherein the propagation velocity is related to α according to one of the following equations:

where c represents the propagation velocity without the viscosity, k represents the diffusibility, v represents the propagation velocity, A represents the cross-sectional area, C represents the capacity per unit length of the transmission line, C (s) represents the frequency-dependent capacity per unit length, G represents the electrical conductivity per unit length of the transmission line, G (s) represents the frequency-dependent electrical conductance per unit length of transmission line, G (s) represents a Laplace transform of approximate Green's thermal conductivity function, K represents thermal conductivity, L represents the inductance per unit length, L (s) represents the frequency-dependent inductance per unit length, R represents the resistance per unit length, R (s) represents the frequency-dependent resistance per unit length, R represents the effective viscosity, μ represents the electrical permeability, ε represents the electrical permittivity, κ represents the thermal conductivity, which represents electrical conductivity, ρ _{0 represents} the equilibrium density, c∞ and c0 represent the velocities of the sound at unlimited frequency or at a frequency of 0, and τ represents a relaxation time. The method of claim 1, wherein an attenuation coefficient of the waveform

is where A, C . C (S), G , G (s), G (s), K, L . L (S), R . R (s), R, c, k, μ, ε, κ, σ, ρ ₀ , c _∞ , c ₀ and τ are as defined in claim 6.